CN1626032A - Time series analysis method of nuclear magnetic resonance for brain functions based on constrained optimization - Google Patents

Abstract

The present invention relates to a time series analysis method of brain function nuclear magnetic resonance based on constraint optimization in the field of nuclear magnetic resonance technology, comprising: step 1: obtaining the time series of functional magnetic resonance; step 2: estimating the hemodynamic function of a single pixel, for step 1 Perform deconvolution operation on the obtained time series; Step 3: Estimate the hemodynamic function of different stimuli, and use the optimization method according to the hemodynamic function of a single pixel estimated in Step 2; Step 4: Statistical hypothesis test, one by one Statistical hypothesis testing was performed on each pixel. It is used for the positioning of brain function before surgery in medical clinics, the diagnosis and prognosis evaluation of brain diseases, the positioning of brain functional areas in brain science research, and the functional connection analysis of brain functional areas.

Description

Brain function nuclear magnetic resonance, NMR Time series analysis method based on constrained optimization

Technical field

The present invention relates to the nuclear magnetic resonance technique field, particularly a kind of brain function nuclear magnetic resonance, NMR Time series analysis method based on constrained optimization, the preoperative brain function that is used for clinical medicine is located, the diagnosis of disease of brain is located with the brain domain in more back assessment, the brain science research and the function of brain domain is connected analysis, belongs to intelligent information processing technology.

Background technology

Since brain function nuclear magnetic resonance, NMR (functional magnetic resonance imaging) fMRI technology was born, the fMRI time series analysis was the popular research direction that fMRI researcher in various countries is paid close attention to always.Usually, fMRI time series analysis algorithm can be divided into model-driven and data-driven two big classes.Because reasonability and ease for use on the physiologic meaning of data-driven method are subjected to various countries neuroscientist's favor gradually.Representative in the Model-driven method is general linear model and contrary convolution model.In brief, general linear model is by artificial specified design matrix the hematodinamics priori to be added in the model, carries out multiple regression analysis again, thereby can obtain the fitness of prior model and fMRI data.Its shortcoming is that the appointment of design matrix is relatively more subjective.Contrary convolution model at first obtains convolution kernel by the contrary convolution algorithm of time series and stimulus sequence, carries out multiple regression analysis again, and promptly its design matrix estimates.Summarize, different tested of general linear model hypothesis, different brain districts have identical hemodynamics variation.Contrary convolution model supposes that then different pixels has different hemodynamics variation.From then on say on the meaning that contrary convolution model more meets the physiology characteristic of human brain.Compare with general linear model,, studies show that the hemodynamics variation between each stimulation (trial) of human brain is different though contrary convolution model has improved sensitivity to a certain extent, just powerless for the contrary convolution model of this situation.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, a kind of new brain function nuclear magnetic resonance, NMR Time series analysis method is proposed, this method is considered the hematodinamics discordance between each stimulation (trial) of human brain, and then improves the accuracy that the brain function active region is detected.The present invention is based on contrary convolution technique and constrained optimization method,, make full use of brain function nuclear magnetic resonance, NMR time serial message, proposed the brain function nuclear magnetic resonance, NMR Time series analysis method of a novelty in conjunction with assumed statistical inspection.Owing to adopted constrained optimization method, in conjunction with the latest developments of brain hematodinamics response investigations, by increase new constraint in model, model itself can be accomplished from expanding.

Proposed by the invention based on optimized brain function nuclear magnetic resonance, NMR time series analysis algorithm, comprise the hemodynamics mathematic(al) function of estimating single pixel, hemodynamics mathematic(al) function and three basic steps of assumed statistical inspection of estimating different stimulated:

1, estimates the hemodynamics mathematic(al) function of single pixel

To each pixel, a time series of following is arranged all.In the method, we think, comprise three kinds of components in this time sequence: the hematodinamics signal that 1) derives from outside stimulus; 2) drift that brings by physiological activities such as breathing, heart beating and magnetic resonance system; 3) noise.We suppose that the hemodynamics variation process is a linear system, that is,

Time series=stimulus sequence  hemodynamics mathematic(al) function+drift+noise

Wherein,  represents convolution algorithm.Utilize contrary convolution technique, by least square method, we can estimate the pairing hemodynamics mathematic(al) function of each pixel.

2, estimate the hemodynamics mathematic(al) function of different stimulated

Based on hemodynamic achievement in research and constrained optimization method, we suppose that the caused hematodinamics response of different stimulations is different.The formula of the hemodynamics mathematic(al) function of calculating different stimulated is as follows:

$\underset{H_j}{\min }{\left|\right|\hat{Z}-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{H}_j\⊗f_j\left|\right|}_2^2----\left(1\right)$

s.t.H _j∈N(h，ε)

Wherein, H _jBe j hemodynamics mathematic(al) function that stimulates, J is the total number that stimulates, Be the time series after deconvoluting, (h ε) represents the neighborhood of h to N, and h is the hemodynamics mathematic(al) function of the single pixel of trying to achieve in the step 1.Based on the basic framework of following formula, we can add another constraints

$\underset{H_j}{\min }{\left|\right|\hat{Z}-\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{H}_j\⊗f_j\left|\right|}_2^2----\left(2\right)$

s.t.H _j∈N(h，ε)

FWHM(H _i)∶FWHM(H _j)＝RT _i∶RT _j，ij

Wherein, FWHM (H _i) be hemodynamics mathematic(al) function H _IFull width at half maximum, RT _iWhen being i reaction that stimulates.

3, assumed statistical inspection

In order to determine whether certain pixel activates, and we carry out assumed statistical inspection.

Null hypothesis:

Alternative hypothesis:

Statistic F is

$F=\frac{\frac{\mathrm{SB}-\mathrm{SF}}{d_B-d_F}}{\frac{\mathrm{SF}}{d_F}}----\left(3\right)$

Wherein, H _MinBe the constrained optimization optimal solution, $\mathrm{SB}={\left|\right|\hat{Z}\left|\right|}_2^2,$ $\mathrm{SF}={\left|\right|\hat{Z}-\underset{J=1}{\overset{J}{\mathrm{\Σ}}}{F}_j\left(H_{\min }\right)\⊗f_j\left|\right|}_2^2,$

d _B＝N-P-2，d _F＝N-P-2-(P+1)。Under null hypothesis, statistic F obeys F (d _B-d _F, d _F) distribute, and bigger F represents that the activated probability of corresponding pixel is big more.

The present invention adopts constrained optimization method, can consider the discordance of hematodinamics response between the different stimulated, and by increasing new constraints, can make our method expand flexibly, be a kind of succinct and effective brain function nuclear magnetic resonance, NMR Time series analysis method.The present invention can be used for preoperative brain function location, the diagnosis in the disease of brain and the more back assessment of clinical medicine, brain domain location and the brain domain function in the brain science research is connected analysis.

Description of drawings

Fig. 1 is the schematic diagram of the brain function nuclear magnetic resonance, NMR Time series analysis method based on constrained optimization of the present invention;

Fig. 2 and Fig. 3 are the selected time series charts of brain function nuclear magnetic resonance, NMR Time series analysis method based on constrained optimization of the present invention.

The specific embodiment

For understanding technical scheme of the present invention better, be further described below in conjunction with accompanying drawing and specific embodiment.

The present invention is based on optimized brain function nuclear magnetic resonance, NMR Time series analysis method principle as shown in Figure 1.

Step 1: obtain the functional MRI time series.Being captured on the magnetic resonance scanner that possesses plane echo-wave imaging (EPI) sequence of brain function nuclear magnetic resonance, NMR time finished.The concrete parameter of imaging does not have specific (special) requirements, but generally is no less than 3 layers, and the sampling time point is generally dozens of or more, and spatial resolution is generally several millimeters, as 3 * 3mm2.

Step 2: the hemodynamics mathematic(al) function of estimating single pixel.The time series that obtains in the step 1 is carried out contrary convolution algorithm, and the result of contrary convolution is the hemodynamics mathematic(al) function of single pixel.

Step 3: the hemodynamics mathematic(al) function of estimating different stimulated.Can estimate the hemodynamics mathematic(al) function of single stimulation according to the hemodynamics mathematic(al) function utilization optimization method (formula (2)) of the single pixel that estimates in the step 2.

Step 4: assumed statistical inspection.One by one each pixel is carried out assumed statistical inspection (formula (3)), and then detect activated pixel.

Among Fig. 2, selected time series such as Fig. 2.Wherein have 13 stimulations, 91 time points.

Among Fig. 3, dotted line is represented primary time series, and solid line is represented the hemodynamics mathematic(al) function of 13 stimulations, and the dotted line point cutting edge of a knife or a sword of below represents to stimulate the time that presents.

Embodiment

1, estimates the hemodynamics mathematic(al) function of single pixel

Selected time series such as Fig. 2.Wherein have 13 stimulations, 91 time points.

We at first estimate the hemodynamics mathematic(al) function of pixel, and the result is: [3.26 5.38 0.50-3.92-3.96-4.46-2.57]

2, estimate the hemodynamics mathematic(al) function of different stimulated

Utilize the hemodynamics mathematic(al) function and the constrained optimization (referring to formula (2)) of the pixel that estimates in the first step, we can obtain the hemodynamics mathematic(al) function (referring to Fig. 3) of each stimulation.

3, assumed statistical inspection

With formula (3), the value of the F statistic of calculating is 18.53, obeys F (7,195) and distributes, and corresponding probit is 2.5618e-018.Generally speaking, be 0.01 if get p-value.Then this pixel is for activating pixel.In addition, compare, obtain following table with traditional contrary convolution method:

Method	The F statistic
		Traditional method (contrary convolution)	16.94
The inventive method	18.53

By comparing, the F statistic of the inventive method is 18.53, and the statistic of the contrary convolution method of tradition is 16.94.As seen, this method is better than traditional contrary convolution method.

Claims (2)

1. A brain function nuclear magnetic resonance time series analysis method based on constraint optimization is characterized in that comprising the hemodynamic function of estimating a single pixel, estimating the hemodynamic function of different stimulations and three basic steps of statistical hypothesis testing: 1) Estimate the hemodynamic function of a single pixel: under the assumption that the hemodynamic change process is a linear system, the hemodynamic function corresponding to each pixel is estimated by using the deconvolution technique and the least square method; 2) Estimate the hemodynamic function of different stimuli: Based on the research results of hemodynamics and the basic framework of the constrained optimization method $\underset{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; min</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ stH _j ∈ N(h, ε) Among them, _Hj is the hemodynamic function of the jth stimulus, J is the total number of stimuli, is the time series after deconvolution, N(h, ε) represents the neighborhood of h, and h is the hemodynamic function of a single pixel obtained in step 1; 3) Statistical hypothesis test: In order to determine whether a certain pixel is activated, we conduct a statistical hypothesis test, Null hypothesis:

Alternative Hypothesis:

Under the null hypothesis, the statistic F obeys the F(d _B -d _F , d _F ) distribution, and a larger F indicates a greater possibility of activation of the corresponding pixel. 2, according to the brain function MRI time series analysis method based on constraint optimization of claim 1, its specific steps are as follows: Step 1: Obtain fMRI time series; Step 2: Estimate the hemodynamic function of a single pixel, and perform deconvolution on the time series obtained in step 1; Step 3: Estimate the hemodynamic function of different stimuli, and use the optimization method according to the hemodynamic function of a single pixel estimated in step 2; Step 4: statistical hypothesis testing, performing statistical hypothesis testing on each pixel one by one.

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